// ∀a, i, b, j. ( a = b → i = j → W (a, i, R(b, j)) = a )
void Egraph::WoRAxiom( Enode * wor )
{
assert( false );
Enode * a = wor->get1st( );
Enode * i = wor->get2nd( );
Enode * worElement = wor->get3rd( );
Enode * b = worElement->get1st( );
Enode * j = worElement->get2nd( );
assert( worElement->isDTypeArrayElement( ) );
assert( a->isDTypeArray( ) );
assert( i->isDTypeArrayIndex( ) );
assert( b->isDTypeArray( ) );
assert( j->isDTypeArrayIndex( ) );
// create term W(a,i,R(b,j))
Enode * select = mkSelect( b, j );
Enode * store = mkStore(a,i,select);
// add clause IF a=b THEN IF i=j THEN W(a,i,R(b,j))=a
// that is (NOT(a=b) OR NOT(i=j) OR W(a,i,R(b,j))=a)
vector< Enode * > v;
Enode * lit1 = mkNot(cons(mkEq(cons(a,cons(b)))));
Enode * lit2 = mkNot(cons(mkEq(cons(i,cons(j)))));
Enode * lit3 = mkEq(cons(store,cons(a)));
v.push_back( lit1 );
v.push_back( lit2 );
v.push_back( lit3 );
#ifdef ARR_VERB
cout << "Axiom WoR -> " << "(or " << lit1 << " " << lit2 << " " << lit3 << " )" << endl;
#endif
splitOnDemand( v, id );
handleArrayAssertedAtomTerm( a );
}
//∀a, i, e, j, f i != j → W (W (a, i, e), j, f ) = W (W (a, j, f ), i, e)
void Egraph::WoWNeqAxiom( Enode * wow )
{
assert( false );
Enode * wowArray = wow->get1st( );
Enode * a = wowArray->get1st( );
Enode * i = wowArray->get2nd( );
Enode * e = wowArray->get3rd( );
Enode * j = wow->get2nd( );
Enode * f = wow->get3rd( );
assert( wowArray->isDTypeArray( ) );
assert( a->isDTypeArray( ) );
assert( i->isDTypeArrayIndex( ) );
assert( e->isDTypeArrayElement( ) );
assert( j->isDTypeArrayIndex( ) );
assert( f->isDTypeArrayElement( ) );
// Case i, j not coincident
if( i != j )
{
// create term W(W(a,j,f),i,e)
Enode * store1 = mkStore(a,j,f);
Enode * store2 = mkStore(store1,i,e);
// add clause IF i!=j THEN W(W(a,i,e),j,f)=W(W(a,j,f),i,e)
// that is (i=j OR W(W(a,i,e),j,f)=W(W(a,j,f),i,e))
vector< Enode * > v;
Enode * lit1 = mkEq(cons(i,cons(j)));
Enode * lit2 = mkEq(cons(wow,cons(store2)));
v.push_back( lit1 );
v.push_back( lit2 );
#ifdef ARR_VERB
cout << "Axiom WoW!= -> " << "(or " << lit1 << " " << lit2 << " )" << endl;
#endif
splitOnDemand( v, id );
handleArrayAssertedAtomTerm(store2);
}
}
// ∀a, i, e, j, f. ( i = j → W ( W ( a, i, e ), j, f ) = W ( a, j, f ) )
void Egraph::WoWEqAxiom( Enode * wow )
{
assert( false );
Enode * wowArray = wow->get1st( );
Enode * a = wowArray->get1st( );
Enode * i = wowArray->get2nd( );
Enode * e = wowArray->get3rd( );
Enode * j = wow->get2nd( );
Enode * f = wow->get3rd( );
assert( wowArray->isDTypeArray( ) );
assert( a->isDTypeArray( ) );
assert( i->isDTypeArrayIndex( ) );
assert( e->isDTypeArrayElement( ) );
assert( j->isDTypeArrayIndex( ) );
assert( f->isDTypeArrayElement( ) );
//i,j not coincident
if( i != j )
{
// create term W(a,j,f)
Enode * store = mkStore( a, j, f );
#ifdef PRODUCE_PROOF
if ( config.gconfig.print_inter > 0 )
{
const uint64_t shared = getIPartitions( a )
& getIPartitions( j )
& getIPartitions( f );
// Mixed can't be one at this point
assert( shared != 1 );
// Set AB-mixed partition if no intersection
if ( shared == 0 )
setIPartitions( store, 1 );
// Otherwise they share something
else
setIPartitions( store, shared );
}
#endif
// add clause IF i=j THEN W(W(a,i,e),j,f)=W(a,j,f)
// that is (NOT(i=j) OR W(W(a,i,e),j,f)=W(a,j,f))
vector< Enode * > v;
Enode * lit1_pos = mkEq( cons( i, cons( j ) ) );
Enode * lit1 = mkNot( cons( lit1_pos ) );
#ifdef PRODUCE_PROOF
if ( config.gconfig.print_inter > 0 )
{
const uint64_t shared = getIPartitions( i )
& getIPartitions( j );
// Mixed can't be one at this point
assert( shared != 1 );
// Set AB-mixed partition if no intersection
if ( shared == 0 )
{
setIPartitions( lit1_pos, 1 );
setIPartitions( lit1, 1 );
}
// Otherwise they share something
else
{
setIPartitions( lit1_pos, shared );
setIPartitions( lit1, shared );
}
}
#endif
Enode * lit2 = mkEq( cons( wow, cons( store ) ) );
#ifdef PRODUCE_PROOF
if ( config.gconfig.print_inter > 0 )
{
const uint64_t shared = getIPartitions( wow )
& getIPartitions( store );
// Mixed can't be one at this point
assert( shared != 1 );
// Set AB-mixed partition if no intersection
if ( shared == 0 )
setIPartitions( lit2, 1 );
// Otherwise they share something
else
setIPartitions( lit2, shared );
}
#endif
v.push_back( lit1 );
v.push_back( lit2 );
#ifdef ARR_VERB
cout << "Axiom WoW= -> " << "(or " << lit1 << " " << lit2 << " )" << endl;
#endif
splitOnDemand( v, id );
handleArrayAssertedAtomTerm( store );
}
}
